Feynman's approach to quantum mechanics: Trajectories,commutation relations and uncertainty principle

Summary In this paper the meaning of trajectory for a quantum-mechanical particle is discussed, starting from the path integral expression of the propagator. By a direct method the trajectories mostly contributing to the total amplitude are found, but it seems impossible to interpret them as paths in the physical space-time; on the contrary, the position-momentum commutation relations directly follow. Moreover, we show that the Heisenberg uncertaint principle can be obtained from the path integral approach. In order to give a better understanding of the characteristic quantum-mechanical features and of the difference from the classical problems, the diffusion equation for a Brownian particle is considered in the first part of the paper. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.